### About Multiplying Rational Expressions:

To multiply two or more rational expressions, we find the product of the numerators and place the result over the product of the denominators. When we are done, we simplify. To divide rational expressions, we multiply the first rational expression by the reciprocal of the second.

Test Objectives

- Demonstrate the ability to simplify a rational expression
- Demonstrate the ability to multiply rational expressions
- Demonstrate the ability to divide rational expressions

#1:

Instructions: Perform each indicated operation.

a)

5n^{2} |
• | 4 |

n + 7 | 5n^{3} + 25n^{2} |

b)

x^{2} + 3x + 2 |
• | x + 8 |

3x + 3 | x + 2 |

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#2:

Instructions: Perform each indicated operation.

a)

9r^{3} - 9r^{2} |
÷ | 2r + 3 |

15 - 15r | 10r + 15 |

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#3:

Instructions: Perform each indicated operation.

a)

6x^{2} - 4x - 10 |
÷ | 2x + 2 |

25 - 9x^{2} |
3x^{2} - 10x - 25 |

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#4:

Instructions: Perform each indicated operation.

a)

r + 8 | • | 6r^{2} + 30r + 36 |

3r + 9 | 2r^{2} - 6r - 20 |

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#5:

Instructions: Perform each indicated operation.

a)

2x^{2} + 10x + 8 |
÷ | 56x^{3} + 24x^{2} |

2x + 2 | 14x^{2} + 6x |

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Written Solutions:

#1:

Solutions:

a)

4 |

(n + 7)(n + 5) |

b)

x + 8 |

3 |

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#2:

Solutions:

a) -3r^{2}

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#3:

Solutions:

a) -(x - 5)

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#4:

Solutions:

a)

r + 8 |

r - 5 |

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#5:

Solutions:

a)

x + 4 |

4x |